Just had an idea while out walking and I wanted to throw it out and see what people thought.

It's a folded up sheet of paper that can be unfolded over and over and over again, increasing in area each time until it becomes impossible to unfold further due to necessity of space and technical ability. The weight increases gradually with each unfolding, and no one is able to get an accurate count of the layers, just that there always seems to be enough for at least seven more unfoldings. It's a reversal of that "You can't fold a piece of paper more than X times" trick.

Is that interesting enough on its own, if there were a few test logs detailing the Foundation's attempts to unfold an acres-wide sheet, then admitting they've reached the limits of their ability to test? If not, I'm trying to think of a hook for what could be written on the paper, revealed more and more each time, which would make us want to open more of it despite being unable to.

This sounds like a really cool idea. Maybe every time you open it (even if it's just the first page) there's a different puzzle/game/whatever, and each unfold reveals a more complex/weird page that is all one game/puzzle. I think if you did something like that it would be easy for other people to write test logs for (like 261, 294, and 914).